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The one-loop effective action and trace anomaly in four dimensions
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The one-loop effective action for a generic set of quantum fields is calculared as a nonlocal expansion in powers of the curvatures (field strengths). This expansion is obtained to third order in the curvature. It is stressed that the covariant vertices are finite. The trace anomaly in four dimensions is obtained directly by varying the effective action. The nonlocal terms in the action, producing the anomaly, contain non-trivial functions of three operator arguments. The trace anomaly is derived also by making the conformal transformation in the heat kernel.
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On the Renormalization in Conformal Quantum Gravity
A formal BRST proof that one-loop divergences in conformal quantum gravity, pure or with matter, are invariant under local conformal transformations.
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